The economy was at risk of a deep recession after the dotcombubble burst in early 2000; this situation was compounded by the September 11 terrorist attacks that followed in 2001. In response, central banks liquidity through a reduction in interest rates. In turn, investors sought higher returns through riskier investments. Lenders took on greater risks too, and approved subprime mortgage loans to borrowers with poor credit. Consumer demand drove the housing bubble to all-time highs in the summer of 2005, which ultimately collapsed in August of 2006. (For an in-depth discussion of these events, see The Fuel That Fed The Subprime Meltdown.)
The end result of these key events was increased foreclosure activity, large lenders and hedge funds around the world tried to stimulate the economy. They created capital declaring bankruptcy, and fears regarding further decreases in economic growth and consumer spending.
Turning Back The Clock
Li was born as Li Xianglin and raised in a rural part of China during the 1960s; his family had been relocated during the Cultural Revolution to a rural village in southern China for "re-education". Li was talented and with hard work he received a master’s degree in economics from Nankai University, one of the country’s most prestigious universities. After leaving China in 1987 at the behest of the Chinese government to learn more about capitalism from the west, he earned an MBA from Laval University in Quebec and a PhD in statistics from the University of Waterloo in Ontario. At this point he changed his name to David X. Li. His financial career began in 1997 at Canadian Imperial Bank of Commerce, and by 2003 he was director and global head of credit derivatives research at Citigroup. In 2004 he moved to Barclays Capital and headed up the credit quantitative analytics team. In 2008 Li moved to Beijing China International Capital Corporation as head of the risk management department.
The Gaussian Copula: What Is It?
One example of a copula often used for modeling in finance—as introduced by David X. Li in 2000—is the Gaussian copula, which is constructed from the bivariate normal distribution via Sklar’s theorem. With Φρ being the standard bivariate normal cumulative distribution function with correlationρ, the Gaussian copula function is
where and Φ denotes the standard normal cumulative distribution function.
Differentiating C yields the copula density function:
is the density function for the standard bivariate Gaussian with Pearson’s product moment correlation coefficient ρ and is the standard normal density.
The Gaussian Copula: What Happened?
For five years, Li’s formula, known as a Gaussian copula function, looked like an unambiguously positive breakthrough, a piece of financial technology that allowed hugely complex risks to be modeled with more ease and accuracy than ever before. With his brilliant spark of mathematical legerdemain, Li made it possible for traders to sell vast quantities of new securities, expanding financial markets to unimaginable levels.
His method was adopted by everybody from bond investors and Wall Street banks to ratings agencies and regulators. And it became so deeply entrenched—and was making people so much money—that warnings about its limitations were largely ignored.
Then the model fell apart. Cracks started appearing early on, when financial markets began behaving in ways that users of Li’s formula hadn’t expected. The cracks became full-fledged canyons in 2008—when ruptures in the financial system’s foundation swallowed up trillions of dollars and put the survival of the global banking system in serious peril.
David X. Li, it’s safe to say, won’t be getting that Nobel anytime soon. One result of the collapse has been the end of financial economics as something to be celebrated rather than feared. And Li’s Gaussian copula formula will go down in history as instrumental in causing the unfathomable losses that brought the world financial system to its knees.
In light of the global economic outlook in the aftermath of the Global Financial Crisis and the current state of accounts, need more be stated to enlighten readers as to how the stage has been set? Granted, investor greed and risk appetite played into a highly clever piece of work.
Copula. (n.d.). Retrieved November 05, 2010, from Wikipedia: The Free Encyclopedia: http://en.wikipedia.org/wiki/Copula_%28statistics%29
David X. Li. (n.d.). Retrieved November 5, 2010, from Wikipedia: The Free Encyclopedia: http://en.wikipedia.org/wiki/David_X._Li
Petroff, E. (2007). Who Is To Blame For The Subprime Mortgage Crisis? Retrieved November 5, 2010, from Investopedia: http://www.investopedia.com/articles/07/subprime-blame.asp
Salmon, F. (2009, February 23). Recipe for Disaster: The Formula That Killed Wall Street. Retrieved November 05, 2010, from Wired.com: http://www.wired.com/techbiz/it/magazine/17-03/wp_quant?currentPage=all